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PRACTICAL MECHANICS FOR BOYS

CHAPTER XII

ON MEASURES

Horse-power.—When work is performed it is designated as horse-power, usually indicated by the letters H. P.; but the unit of work is called a foot pound.

If one pound should be lifted 550 feet in one second, or 550 pounds one foot in the same time, it would be designated as one horse-power. For that reason it is called a foot pound. Instead of using the figure to indicate the power exerted during one minute of time, the time is taken for a minute, in all calculations, so that 550 multiplied by the number of seconds, 60, in a minute, equals 33,000 foot pounds.

Foot Pounds.—The calculation of horse-power is in a large measure arbitrary. It was determined in this way: Experiments show that the heat expended in vaporizing 34 pounds of water per hour, develops a force equal to 33,000 foot pounds; and since it takes about 4 pounds of coal per hour to vaporize that amount of water, the heat developed by that quantity of coal develops the same force as that exercised by an average horse exerting his strength at ordinary work.

All power is expressed in foot pounds. Suppose a cannon ball of sufficient weight and speed strikes an object. If the impact should indicate 33,000 pounds it would not mean that the force employed was one horse-power, but that many foot pounds.

If there should be 60 impacts of 550 pounds each within a minute, it might be said that it would be equal to 1 horse-power, but the correct way to express it would be foot pounds.

So in every calculation, where power is to be calculated, first find out how many foot pounds are developed, and then use the unit of measure, 33,000, as the divisor to get the horse-power, if you wish to express it in that way.

It must be understood, therefore, that horse-power is a simple unit of work, whereas a foot pound is a compound unit formed of a foot paired with the weight of a pound.

Energy.—Now work and energy are two different things. Work is the overcoming of resistance of any kind, either by causing or changing motion, or maintaining it against the action of some other force.

Energy, on the other hand, is the power of doing work. Falling water possesses energy; so does a stone poised on the edge of a cliff. In the case of water, it is called kinetic energy; in the stone potential energy. A pound of pressure against the stone will cause the latter, in falling, to develop an enormous energy; so it will be seen that this property resides, or is within the thing itself. It will be well to remember these definitions.

How to Find Out the Power Developed.—The measure of power produced by an engine, or other source, is so interesting to boys that a sketch is given of a Prony Brake, which is the simplest form of the Dynamometer, as these measuring machines are called.

Fig. 133. Prony Brake

In the drawing (A) is the shaft, with a pulley (A´), which turns in the direction of the arrow (B). C is a lever which may be of any length. This has a block (C´), which fits on the pulley, and below the shaft, and surrounding it, are blocks (D) held against the pulley by a chain (E), the ends of the chain being attached to bolts (F) which pass through the block (C´) and lever (C).

Nuts (G) serve to draw the bolts upwardly and thus tighten the blocks against the shaft. The free end of the lever has stops (H) above and below, so as to limit its movement. Weights (I) are suspended from the end of the lever.

Fig. 134. Speed Indicator

The Test.—The test is made as follows: The shaft is set in motion, and the nuts are tightened until its full power at the required speed is balanced by the weight put on the platform.

The following calculation can then be made:

For our present purpose we shall assume that the diameter of the pulley (A´) is 4 inches; the length of the lever (C), 3 feet; the speed of the shaft (A) and the pulley, 210 revolutions per minute; and the weight 600 pounds.

Now proceed as follows:

(1) Multiply the diameter of the pulley (A´) (4 inches) by 3.1416, and this will give the circumference 12.5664 inches; or, 1.0472 feet.

(2) Multiply this product (1.0472) by the revolutions per minute. 1.0472 × 210 = 219.912. This equals the speed of the periphery of the pulley.

(3) The next step is to get the length of the lever (C) from the center of the shaft (A) to the point from which the weights are suspended, and divide this by one-half of the diameter of the pulley (A´). 36" ÷ 2" = 18", or 1 1/2 feet. This is the leverage.

(4) Then multiply the weight in pounds by the leverage. 600 × 1 1/2 = 900.

(5) Next multiply this product (900) by the speed, 900 × 219.912 = 197,920.8, which means foot pounds.

(6) As each horse-power has 33,000 foot pounds, the last product should be divided by this figure, and we have 197,920.8 ÷ 33,000 = 5.99 H. P.

The Foot Measure.—How long is a foot, and what is it determined by? It is an arbitrary measure. The human foot is the basis of the measurement. But what is the length of a man's foot? It varied in different countries from 9 to 21 inches.

In England, in early days, it was defined as a measure of length consisting of 12 inches, or 36 barleycorns laid end to end. But barleycorns differ in length as well as the human foot, so the standard adopted is without any real foundation or reason.

Weight.—To determine weight, however, a scientific standard was adopted. A gallon contains 8.33 pounds avoirdupois weight of distilled water. This gallon is divided up in two ways; one by weight, and the other by measurement.

Each gallon contains 231 cubic inches of distilled water. As it has four quarts, each quart has 57 3/4 cubic inches, and as each quart is comprised of two pints, each pint has nearly 29 cubic inches.

The Gallon.—The legal gallon in the United States is equal to a cylindrical measure 7 inches in diameter and 6 inches deep.

Notwithstanding the weights and dimensions of solids and liquids are thus fixed by following a scientific standard, the divisions into scruples, grains, pennyweights and tons, as well as cutting them up into pints, quarts and other units, is done without any system, and for this reason the need of a uniform method has been long considered by every country.

The Metric System.—As early as 1528, Fernal, a French physician, suggested the metric system. Our own government recognized the value of this plan when it established the system of coinage.

The principle lies in fixing a unit, such as a dollar, or a pound, or a foot, and then making all divisions, or addition, in multiples of ten. Thus, we have one mill; ten mills to make a dime; ten dimes to make a dollar, and so on.

Basis of Measurement.—The question arose, what to use as the basis of measurement, and it was proposed to use the earth itself, as the measure. For this purpose the meridian line running around the earth at the latitude of Paris was selected.

One-quarter of this measurement around the globe was found to be 393,707,900 inches, and this was divided into 10,000,000 parts. Each part, therefore, was a little over 39.37 inches in length, and this was called a meter, which means measure.

A decimeter is one-tenth of that, namely, 3.937 inches; and a decameter 39.37, or ten times the meter, and so on.

For convenience the metrical table is given, showing lengths in feet and inches, in which only three decimal points are used.

Metrical Table, showing measurements in feet and inches:

METRICAL TABLE, SHOWING MEASUREMENTS IN FEET
AND INCHES

METRIC SYSTEM, SHOWING THE EQUIVALENTS
IN OUR MEASURES